1. Field of the Invention
The invention relates to motor control and more particularly, to motor control applications requiring rapid, periodic, point-to-point movement.
2. Description of the Related Art
Rapid repositioning of an object being moved is accomplished using a motorized system, such as a servo system, that typically is controlled using one of the many known closed-loop control algorithms. A motor and the object moved by the motor are commonly referred to as a xe2x80x9cplant.xe2x80x9d An example of such a plant is a rotating mirror that directs an image into a camera mounted in a weather satellite in which the camera photographs the earth. The motor periodically repositions the mirror to produce a series of photographs that together form an image of the earth. When variations in the plant are expected, adaptive control methods can be used to more accurately position the plant. When the movement is periodic, more specialized adaptive methods, including repetitive and learning control, are available.
Some modern periodic control systems require repositioning times that approach the minimum theoretically possible while also minimizing the peak power used. This requires a minimum-time, optimal solution that generally satisfies Pontryagin""s minimum principle, described, for example, in Optimal Control Theory, Donald E. Kirk, Prentice-Hall Inc., pp. 227-228, 1970. This minimum-time, optimal solution requires an initial maximum acceleration followed by a maximum deceleration and is referred to in the art as bang-bang control. Bang-bang control is usually associated with anxe2x96xa1open-loop control system. In theory bang-bang control moves a plant in a minimum amount of time. However, in practice overshoot and settling after the plant reaches its final position often occur. Variation from the desired position after the initial rapid movement from the bang-bang control usually has sinusoidal components that are referred to as residual vibration. This is a non-zero position error at the end of the bang-bang control operation, the amount of which oscillates as a damped sinusoid around the desired position as a result of the closed loop control moving the plant to eliminate the error. The residual vibration is due to disturbances, non-linlinear effects, resonance, time-related variations and other factors. Frequently, these factors cannot be accounted for, to the precision required, in a model of the control system.
Open-loop control techniques are common in the literature and have been shown to be effective in several areas of control. For example, open-loop control has been used with an input that is based on a plant model for a precision diamond turning application. In that application a hybrid (open and closed-loop) control law could be used. In another example, open-loop control has been used with a switching zone controller that causes motor torque to switch linearly from a maximum positive (acceleration) to a maximum negative (deceleration) value in a robotic application. In yet another example, a xe2x80x9cmodified bang-bangxe2x80x9d controller uses open-loop control for rapid movement and switches to closed-loop control near the desired position to control a (military) tank gun-loader.
Conventional open-loop and open-loop/closed-loop systems, such as those discussed above, do not suffice in applications requiring rapid, periodic movement because they do not simultaneously minimize repositioning time, the peak power used and any residual vibrations. More particularly, they do not include algorithmic, repetitive tuning of open-loop input pulse amplitudes to the motor based upon position and velocity when the loop is closed to minimize residual vibrations resulting from closed-loop control.
The invention can solve the concurrent problems with conventional control systems of minimizing repositioning time, minimizing peak power used, and minimizing residual vibrations for a periodic system requiring rapid movement. Those problems can be solved by using an open-loop command such as a bang-bang control signal that is input to move the plant, then using closed-loop control to fine tune the movement to the desired position, and using a form of repetitive/learning control to adjust the bang-bang control signal parameters for subsequent periodic movements. The open-loop bang-bang control signal is determined to minimize saturation non-linearities in the electronics (e.g., due to peak voltages/currents) and in the motor (e.g., due to acceleration limits). The initial positive and negative amplitudes of the open-loop bang-bang input signal are calculated based on a model of the plant. The maximum and minimum amplitudes of the bang-bang input signal are then adjusted periodically using the repetitive/learning control.
There are advantages to using open-loop control switched to closed-loop control in applications requiring rapid, periodic movement, including the following.
1. Open-loop control can provide faster response than closed-loop control because the command signal input is coupled directly into the plant.
2. Open-loop control can be more efficient than closed-loop control because there are fewer components and response can be closer to time-optimal for point-to-point movement.
3. Linearity (no saturation) within the electronics and the plant (motor) can be maintained by limiting the highest frequency component and the maximum amplitude of the open-loop input command.
4. Closed-loop control reduces the effect of external disturbances and accurately holds the final position after the open-loop movement.